Learning differential equations

In summary, a member introduced themselves and mentioned they would now be able to contribute academically since they have finished their first year of engineering. They asked for advice on how to prepare for four courses involving differential equations and Maxwell's equations. Another member recommended purchasing a DE book and a Schaum's outline for practice problems. They also suggested a textbook for PDEs and mentioned another book with comprehensive problems.
  • #1
theomicron
4
0
Hi everyone,

First, I'll apologize if this is posted in the wrong forum; I couldn't see any more fitting categories.

Secondly, I just wanted to introduce myself. I've been a member for a little over a year, but haven't contributed since I didn't think I had anything useful to contribute academic wise; now that I've finished my first year of engineering, I can help answer some of the more basic calculus questions.

My main question is this: next year I am being thrown head first into four courses all dealing with DEs (in all forms) and maxwell's equations. What is the best way to learn/prepare for differential equations? I understand that they present a very solid foundation for later courses so they're very important.

Cheers!
 
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  • #2
I would say buy the DE book now and start grinding away. I would also recommend getting the Schaum's outline entitled "Modern Introductory Differential Equations". It has many problems with detailed solutions, and even more problems with just the answers.
 
  • #3
Great! Thanks for the quick response. I'll see if I can find a copy of Schaums somewhere. Do you happen to know if that covers PDEs as well?
 
  • #4
It doesn't but there's another Schaum's outline entitled "Partial Differential Equations". I have them both, and I like them. If you want an honest-to-goodness textbook on PDE's I would recommend Strauss. It's the one I was taught from, and I really liked it.
 
  • #5
Another good one to look at might be "Ordinary Differential Equations" by Pollard and Tenenbaum. Lots of problems, and quite comprehensive. (And it's a Dover, so it's pretty cheap.)
 

1. What are differential equations?

Differential equations are mathematical equations that describe the relationship between a function and its derivatives. They are used to model many real-world phenomena, such as the growth of populations, the flow of fluids, and the behavior of electrical circuits.

2. Why is learning differential equations important?

Learning differential equations is important because it allows us to understand and predict the behavior of complex systems in the natural and physical world. It is also a fundamental tool in many fields of science, engineering, and economics.

3. What are some common methods for solving differential equations?

Some common methods for solving differential equations include separation of variables, substitution, and using integrating factors. There are also numerical methods, such as Euler's method and Runge-Kutta methods, which use approximations to solve differential equations.

4. How can I improve my skills in solving differential equations?

To improve your skills in solving differential equations, it is important to have a strong foundation in calculus and algebra. Practice is also key - solving a variety of problems and studying different methods will help you become more proficient. Additionally, seeking out resources such as textbooks, online lectures, and practice problems can also be helpful.

5. Are there any applications of differential equations in everyday life?

Yes, differential equations have many applications in everyday life, such as predicting weather patterns, modeling traffic flow, and analyzing economic trends. They are also used in the fields of medicine, biology, and psychology to understand and predict the behavior of complex systems in the human body and mind.

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